I am interested in the Bounded Pareto Distribution but I can't find any reference that supplies me the moment generating function. This does however seem like something that is known.

More general : Is there some (online/book/...) reference where I can find a list of all (or at least many) distributions and their most important properties (like moments, PDF, CDF,...) I have been mainly using wikipedia but it has now let me down.

EDIT:

From the provided comment, I have found that a general formula for the moment generating formula for the MGF might not be avaible. I do however still wonder how to obtain it numerically. When I use the moments (for which there does exist a general formula) and the taylor series expansion to obtain the MGF, I find that (when the upper bound is somewhat large) the moments quickly explode and (at least numerically) the Taylor series diverges.

To obtain the $k$-th moment one would usually differentiate $k$ times and then set $t=0$ but that won't work with this MGF. If $\alpha$ is not a positive integer, then you'll need to take the $k$-th derivative followed by taking the limit of that derivative as $t\rightarrow 0$. Using Mathematica commands that translates to the following when $k=3$: